A body is projected vertically upward from the surface of the earth with a velocity equal to half the escape velocity. If fi is the radius of the earth, the maximum height attained by the body is

initial K.E. =12mv2=12mve22=18mve2=GmM4R ∵ve=2MGRP.E.=−GmMRTotal Energy =GmM4R−GmMR=−3GmM4R……………….(1)Lot the body come to rest at a height r from the centre of the earth. Now its energy is given by Final energy=−GmMr………..(2)Comparing eqs. (1) and (2), we getr=(4R/3)∴Maximum height attained=r−R=(4R/3)−R=(R/3)